Name
8-1
Date
Ratios and Rates (pages 312–315)
1, 2, 36,
Q 41, 48
C
C
You can compare two quantities by using a ratio. A common way to express
a ratio is as a fraction in simplest form. If the two quantities you are
comparing have different units of measure, this kind of ratio is called a
rate. A rate is in the form of a unit rate when the denominator is 1.
Writing a Rate
and a Unit Rate
A rate is a ratio of two measurements that have different units. To write a
ratio as a unit rate, divide the numerator and denominator by the same
number to rewrite the ratio as a fraction with a denominator of 1.
EXAMPLES
A Write the ratio in three different ways:
5 sixth-graders out of 15 students.
Express this ratio as a fraction in
simplest form.
As a fraction
B Express the ratio as a unit rate: 15
pencils for $5. How many pencils can
you buy for $1?
Write the ratio as a fraction.
5
15
To rewrite the fraction with a denominator of 1,
divide numerator and denominator by 5.
As a ratio
5:15
In words
5 to 15
Another way is in the problem: 5 out of 15.
5
15
in simplest form is
15 pencils
$5
15 pencils
$5
15
pencils
5
or 3 pencils for $1
$1
1
.
3
Try These Together
1. Write the ratio in three different ways:
7 sodas out of 20 are sugar free.
2. Express the ratio as a rate: $14.50 for
5 rides. What is the cost for one ride?
HINT: Write the numbers in the same order as
they appear in the problem.
HINT: Divide numerator and denominator by 5.
PRACTICE
Express each ratio as a fraction in simplest form.
3. 4 out of 16 papers are typed
4. 5 out of 10 horses are white
5. 7 blue bicycles out of 21 bicycles
6. 4 watermelons out of 10 melons
Express each ratio as a rate.
7. $1.50 for 3 bottles of juice
B
C
C
B
C
9. Standardized Test Practice If milk costs $5.50 for 2 gallons, how much
does it cost per gallon?
A $11.00
B $10.50
C $2.75
D $3.50
5. 3
1
6. 5
2
7. $0.50 per bottle of juice
B
A
1
8.
4. 2
A
7.
© Glencoe/McGraw-Hill
64
$14.50
1
2. or $2.90 per ride 3. 5 rides
4
B
6.
7
A
5.
Answers: 1. 7:20, 7 to 20; 20
4.
8. $5.00 per bracelet 9. C
3.
8. 5 bracelets for $25.00
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-2
Date
Solving Proportions
1, 3, 4, 10,
Q 34,41,37,47,
C 49,
C 51
(pages 317–320)
A proportion is an equation that shows that two ratios are equivalent. The
a
c
general form of a proportion is b d , where neither b nor d is equal to
zero. The cross products of a proportion are ad and bc.
Property of
Proportions
The cross products of a proportion are equal.
c
a
If , then ad bc.
b
d
EXAMPLES
A Use cross products to find out whether
this pair of ratios forms a proportion.
Write the cross products.
2 21 7 y
42 7y
3 9
, 4 12
Does
3
4
9
?
12
Are the cross products equal?
42
7
Does 3 12 4 9? Yes, because 36 36.
3
4
9
12
y
2
B Solve the proportion for y.
7
21
7y
7
Divide each side of the equation
by 7.
6y
The solution is 6.
is a proportion because the cross
products are equal.
Try These Together
1. Use cross products to determine
whether this pair of ratios forms a
0.5 0.4
proportion. ,
2
1.6
3
4
.
2. Solve the proportion p
20
HINT: Set the cross products equal to each
other and solve for p.
HINT: Write the proportion with a ? over the ,
and test to see if the cross products are really
equal.
PRACTICE
Determine whether each pair of ratios forms a proportion.
1 5
3. 2 , 10
4 2
4. 8 , 4
8 2
6. ,
13 5
4 1
5. 5 , 8
Solve each proportion.
3
x
7. 6 2
B
A
9. 8 10. 5 11. B
8.
7. 1 8. 22
7.
11. Standardized Test Practice The home economics class is making a
casserole. They need 3 eggs for 1 casserole. How many eggs do they
need for 4 casseroles?
A 9
B 12
C 15
D 10
© Glencoe/McGraw-Hill
65
6. no
C
5. no
A
4. yes
C
B
B
6.
3. yes
C
A
5.
d
2
10. 25
10
2. 15
4.
9
6
9. z
12
Answers: 1. yes
B
3.
4
2
8. w
11
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-3
Date
Scale Drawings (pages 324–327)
1, 2, 37,
Q 41,4947,
C
C
A scale drawing is exactly the same shape as an object, but the drawing
may be larger or smaller than the real object. When you know the length in
a scale drawing, you can use a proportion to find the actual length, .
Reading a
Scale Drawing
The scale written on the drawing or model gives the ratio that compares the
lengths on the drawing to the actual lengths of the object. Use the scale of
the drawing for one of the ratios and the known and unknown lengths for
the other ratio. Write a proportion and solve it for the unknown length.
EXAMPLES
A A model car has a scale of 1:16. A
1
window on the model measures of a
32
meter. What will this same window
measure on the real car?
1
16
1
32
meter
16 meter
32
1
1
2
meter
B The doorway of an actual house
measures 3 ft wide. How wide will the
doorway in a model house be if the scale
is 1 ft 2 in.?
1 ft
2 in.
Write a proportion.
3 ft
so 1 x 6 or 6.
The model doorway will be 6 inches wide.
Find cross products.
Solve.
The actual window measures
1
2
meter.
Try These Together
1. The scale of a map is 1 inch 25 miles.
The distance on the map between two
cities is 7 inches. How many miles apart
are they?
HINT: Write a proportion using
1
25
2. A line on a scale drawing of a building
measures 15 inches. The same length on
the actual building is 5 yards. What is
the scale of the drawing in simplest form?
as one ratio.
HINT: One ratio is
15
5
and the other is
x inches
.
1 yard
PRACTICE
3. Transportation The oldest monorail system in the world is in
Wuppertal, Germany. Its track is 8.5 miles long. If you wanted to build a
model of the track that has a scale of 1 inch 0.5 miles, how long would
the model track be?
B
C
C
B
C
B
6.
A
7.
8.
B
A
4. Standardized Test Practice Mavis and Reese want to rearrange the
furniture in their living room. Before they move the furniture, they make
a model. The scale for the model is 1 inch 2 feet. If their sofa is
actually 6 feet long, how long is the model of the sofa?
A 3 inches
B 4 inches
C 3 feet
D 4 feet
4. A
A
5.
© Glencoe/McGraw-Hill
66
2. 3 inches to 1 yard 3. 17 inches
4.
Answers: 1. 175 miles
3.
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-4
Date
Percents and Fractions
1, 2, 10,
Q 29,34,30,37,
C 41
C
(pages 330–333)
A percent is a ratio that compares a number to 100.
Expressing
a Percent as
a Fraction
To write a percent as a fraction, follow these steps.
• Express the percent as a fraction with a denominator of 100.
• Simplify the fraction.
To write a fraction as a percent, follow these steps.
x
• Set up a proportion with the fraction as one ratio and as the other.
100
Expressing
a Fraction
as a Percent
• Find the cross products and divide to solve for x. The fraction is equal to
x percent.
EXAMPLES
14
B Express the fraction as a percent.
25
A Express 75% as a fraction in simplest
form.
75% is
75
.
100
75% 75
100
75% 3
4
14
25
x
100
1,400 25x
1,400
25
Divide numerator and denominator
by the common factor of 25.
x
56 x, so
Write a proportion.
Find the cross products.
Divide to solve for x.
14
25
56%
Try These Together
13
1. Express the fraction as a percent.
20
2. Express 120% as a fraction in simplest form.
HINT: Write a proportion and solve for x.
HINT: Begin with the fraction
120
.
100
PRACTICE
Express each percent as a fraction in simplest form.
3. 25%
4. 10%
5. 30%
7. 60%
8. 95%
9. 16%
6. 45%
10. 58%
Express each fraction as a percent.
B
36
16. 40
8
17. 40
7
18. 5
C
19. Standardized Test Practice What is 24% expressed as a fraction in
simplest form?
24
C 100
6
D 25
3. 4
1
4. 10
1
5. 10
3
6. 20
9
7. 5
3
8. 20
19
67
1
19. D
9. 25
4
10. 50
29
11. 50%
12. 160 %
13. 75%
14. 44%
© Glencoe/McGraw-Hill
2. 1 5
12
B 50
Answers: 1. 65%
18
A 75
18. 140%
B
A
17. 20%
B
8.
12
15. 20
C
B
A
7.
44
14. 100
C
A
5.
6.
3
13. 4
16. 90%
4.
8
12. 5
15. 60%
3.
1
11. 2
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-5
Date
Percents and Decimals
(pages 334–336)
1, 10, 30,
Q 34, 41
C
C
You have seen that percents can be written as fractions. Percents can also
be written as decimals, and decimals can be written as percents.
Writing a
Percent as
a Decimal
To write a percent as a decimal, follow these steps.
• Rewrite the percent as a fraction with a denominator of 100.
• Express the fraction as a decimal.
Writing a
Decimal as
a Percent
To write a decimal as a percent, follow these steps.
• Rewrite the decimal as a fraction with a denominator of 100.
• Express the fraction as a percent.
EXAMPLES
A Express 56% as a decimal.
56% 56
100
B Express 0.84 as a percent.
0.84 which is 0.56
C Express 0.35% as a decimal.
0.35% 0.35
100
Multiply by
100
100
which is 84%
D Express 0.103 as a percent.
0.103 to get rid of
the decimal in the numerator.
35
10,000
84
100
which is 0.0035
Try These Together
1. Express 0.4% as a decimal.
103
1,000
10.3
100
Divide numerator and
denominator by 10.
which is 10.3%
2. Express 0.09 as a percent.
HINT: Rewrite as a fraction with a
denominator of 100. Then multiply
numerator and denominator by 10.
HINT: Rewrite as a fraction with a denominator
of 100.
PRACTICE
B
14. 0.61
18. 0.063
C
19. Standardized Test Practice In a taste test at a grocery store, people were
given a chip with salsa on it and asked if they would buy the salsa. Of
those who answered, 67% said “yes.” Express this percent as a decimal.
A 0.22
B 0.67
C 0.34
D 0.50
10. 0.345
11. 14%
12. 87%
B
A
9. 0.11
B
8.
13. 0.25
17. 0.73
C
B
A
7.
Express each decimal as a percent.
11. 0.14
12. 0.87
15. 0.59
16. 0.12
C
A
5.
6.
6. 55%
10. 34.5%
8. 0.91
4.
5. 46%
9. 11%
Answers: 1. 0.004 2. 9% 3. 0.27 4. 0.18 5. 0.46 6. 0.55 7. 0.72
13. 25% 14. 61% 15. 59% 16. 12% 17. 73% 18. 6.3% 19. B
3.
Express each percent as a decimal.
3. 27%
4. 18%
7. 72%
8. 91%
© Glencoe/McGraw-Hill
68
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-6
Date
Estimating with Percents
(pages 337–339)
1, 41, 48
Q
C
C
When a problem asks for “about how many,” the word about tells you that
an exact answer is not needed. You can estimate the answer.
Memorizing these common equivalents will help you estimate.
Often you can think of money to help you remember these.
Common Equivalents
for Percents and
Fractions
1
For example: A quarter is $0.25 which is of a dollar.
4
1
20% 5
1
25% 4
1
1
12 %
2
8
1
2
16 %
3
6
2
40% 5
1
50% 2
1
3
37 %
2
8
1
1
33 %
3
3
3
60% 5
3
75% 4
1
5
62 %
2
8
2
2
66 %
3
3
4
80% 5
100% 1
1
7
87 %
2
8
5
1
83 %
3
6
EXAMPLES
A Estimate 61% of 35.
B Estimate 9% of 415.
The table shows that 60% is
3
5
3
.
5
Multiply to estimate.
10% is
1
10
35 21. So 61% of 35 is about 21.
Try These Together
1. Estimate 88% of 64.
HINT: Multiply to find
7
8
1
.
10
Multiply to estimate.
415 41.5. So 9% of 415 is about 41.
2. Estimate 17% of 24.
of 64.
HINT: Multiply to find
1
6
of 24.
PRACTICE
Estimate each percent.
3. 26% of 40
4. 18% of 10
7. 73% of 104
8. 80% of 51
11. 34% of 9
12. 11% of 80
5. 48% of 30
9. 101% of 41
13. 58% of 25
6. 60% of 21
10. 22% of 80
14. 19% of 45
15. About how much is 48% of 12?
16. Estimate 24% of 200.
17. School There are 23 students in Donovan’s class. About 25% of his classmates are
older than him. Estimate how many of Donovan’s classmates are older than him.
B
C
C
18. Standardized Test Practice Tyler’s family gets a busy signal 21% of the
time they try to log on to the Internet. If they tried to log on 10 times in
one day, about how many times would they get a busy signal?
A 2
B 3
C 4
D 5
9. 41
10. 16
11. 3 12. 8 13. 15
C
B
A
8. 40
8.
7. 75
A
7.
6. 12
B
B
6.
4. 2 5. 15
A
5.
© Glencoe/McGraw-Hill
69
2. 4 3. 10
4.
Answers: Sample answers are given. 1. 56
14. 9 15. 6 16. 50 17. 6 18. A
3.
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
Name
8-7
Date
Percent of a Number
1, 11, 41,
Q 47, 48
C
C
(pages 340–343)
To find the percent of a number, you can change the percent to a fraction or
to a decimal, and then multiply by the number. You can also use a
calculator.
Finding the Percent
of a Number
• Method 1: Change the percent to a fraction and multiply.
• Method 2: Change the percent to a decimal and multiply.
EXAMPLES
A Find 25% of 56.
25% 1
4
B Find 103% of 60.
1
4
103% 25% of 56 is 14.
Try These Together
1. Find 0.5% of 30.
HINT: Rewrite the percent as
5
1,000
which is 1.03
1.03 60 61.8
103% of 60 is 61.8.
Notice that when you take a percent greater
than 100 of a number, the answer is greater
than the number.
56 14
then as
103
100
2. Find 7% of 40.
0.5
100
and
HINT: Rewrite 7% as
7
100
or 0.07.
or 0.005. Then multiply.
PRACTICE
Find the percent of each number.
3. 25% of 20
4. 40% of 65
7. 80% of 120
8. 75% of 64
11. 33% of 300
12. 20% of 120
5. 35% of 80
9. 10% of 70
13. 50% of 64
6. 60% of 35
10. 20% of 45
14. 90% of 60
15. What is 90% of 70?
16. Find 80% of 80.
17. Games 75% of the games sold at a game store are board games. If the
game store sold 256 games in one day, how many of those games were
board games?
18. Banking Catalina’s mother went to the bank to take out $40.00. She
asked for 50% of the $40.00 in dollar bills. How much money did she
receive in dollar bills?
B
C
C
19. Standardized Test Practice What is 30% of 90?
A 27
B 30
C 33
12. 24
13. 32
14. 54
15. 63
C
B
A
9. 7 10. 9 11. 99
8.
D 24
8. 48
A
7.
7. 96
B
B
6.
70
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1
© Glencoe/McGraw-Hill
6. 21
A
5.
5. 28
4.
Answers: 1. 0.15 2. 2.8 3. 5 4. 26
16. 64 17. 192 18. $20.00 19. A
3.
Name
8
Date
Chapter 8 Review
Ratio Treasure
Use the treasure map to answer the following questions.
Treasure
3 cm
N
5 cm
Windmill
4 cm
1 cm = 12 m
You are here.
1. You’re using the map to find a hidden treasure. If you walk directly to the
treasure, how far will you walk?
2. To make sure you find the treasure, you decide to use a compass to walk
north to the windmill first, then east to the treasure. How far are you
from the windmill? How far is the windmill from the treasure?
3. Suppose instead that you are 60 meters south of a boulder, and the
boulder is 80 meters west of a buried treasure. Draw a treasure map with
a scale of 1 cm 20 m. Be sure to label distances on your map
according to the scale.
Answers are located on p. 109.
© Glencoe/McGraw-Hill
71
Georgia Parent and Student Study Guide
Mathematics: Applications and Connections, Course 1